Hi, I was wondering what happens if one has a photon that is so energetic that it gets trapped in its own gravitational field. Imagine a mass m orbitting a large mass M in a circular orbit with radius r and with transverse velocity v. By equating the gravitational force on m with its centripetal acceleration we have: G M m / r^2 = m v^2 / r Now let velocity v approach the speed of light c. The mass m will be boosted by a Lorentz factor but I think the equation should still hold so that we have: G M m / r^2 = m c^2 / r Thus cancelling m we have: M = (c^2 / G) r or in terms of Energy E = M c^2 we have E = (c^4 / G) r (*) This is the energy that a photon must have to get trapped in its own gravitational field so that it orbits in a circle with radius r. The quantitiy c^4 / G is also the string tension so maybe this is also a model of a string. Now let us suppose that the photon has angular momentum hbar. Then we have r * p = hbar where p is the linear momentum of the photon. Now we know that p = E / c for photons so that we have: r * E / c = hbar E = hbar * c / r E = h * c / 2.pi.r E = h / t (**) where t is the time period of the photon orbit. If we substitute E=h/t into equation (*) we get: h / t = (c^4 / G) * r Rearranging we get: r * t = h G / c^4 Thus we find that the spacetime area occupied by this bound photon, r * t, is quantized. I was wondering if this is similar to the result that the world sheet area swept out by strings is quantized.